I am looking for a Thai mobile phone provider that will let me turn off the mailbox completely!

I.e. I wish the call to be terminated without message if the phone is switched off, not in range or if I refuse the call.

From your experience, is that possible ?

As far as I know all mobile carriers in Thailand have these options. You have to set them from the phone though (normally under "settings" -> "call settings" or similar).

On DTAC what you wish for is the default setting. I had to request for both the voicemail service and missed call SMS to be activated.

excellent, thanks!

many of our European providers play music or messages so that the caller will pay a connection.

not so funny when you redirect your own voip phone to the Thai mobile...

It is not exactly what you are looking for but AIS/One-2-Call do offer a Call Screening Service , which also includes blocking.